Article ID Journal Published Year Pages File Type
4584070 Journal of Algebra 2015 31 Pages PDF
Abstract

Let Γ   be a generic subgroup of the multiplicative group C⁎C⁎ of nonzero complex numbers. We define a class of Lie algebras associated to Γ, called twisted Γ-Lie algebras, which are natural generalizations of the twisted affine Lie algebras. Starting from an arbitrary even sublattice Q   of ZNZN and an arbitrary finite order isometry of ZNZN preserving Q, we construct a family of twisted Γ-vertex operators acting on generalized Fock spaces which afford irreducible representations for certain twisted Γ-Lie algebras. As an application, this recovers a number of known vertex operator realizations for infinite dimensional Lie algebras, such as twisted affine Lie algebras, extended affine Lie algebras of type A, trigonometric Lie algebras of series A and B, unitary Lie algebras, and BC-graded Lie algebras.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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